INTRODUCTION
Scientific Calculator
|
|
The calculator was written by Rolf Howarth in early 1996.
A fully featured scientific calculator with proper operator precedence is implemented, including trig functions and logarithms, factorials, 12 levels of parentheses, logs to base 2 (a handy function for information entropists!), bitwise logical operators, hex, octal, binary and ASCII display.
The calculator is written in JavaScript and you are welcome to view the JavaScript source (visible within the HTML page) for personal educational purposes as long as you recognize that it is copyrighted and not in the public domain. This calculator is now available as part of Hummingbird's Enterprise Information Portal. All enquiries regarding licensing the calculator should be directed to Hummingbird Ltd.
Basic Functions
Addition
The addition (sum function) is used by clicking on the "+" button or using the keyboard. The function results in a+b.
Subtraction
The subtraction (minus function) is used by clicking on the "-" button or using the keyboard. The function results in a-b.
Multiplication
The multiplication (times function) is used by clicking on the "x" button or using the keyboard "*" key. The function results in a*b.
Division
The division (divide function) is used by clicking on the "/" button or using the keyboard "/" key. The function results in a/b.
Sign
The sign key (negative key) is used by clicking on the "(-)" button. The function results in -1*x.
Square
The square function is used by clicking on the "x^2" button or type "^2". The function results in x*x.
Square Root
The square root function is used by clicking on the "x" button or type "sqrt()". This function represents x^.5 where the result squared is equal to x.
Raise to the Power
The raise to the power (y raised to the x function) is used by clicking on the "y^x" button or type "^".
Natural Exponential
The natural exponential (e raised to the x) is used by clicking on the "e^x" button or type "exp()". The result is e (2.71828...) raised to x.
Logarithm
The logarithm (LOG) is used by clicking on the "LOG" button or type "LOG()".
Natural Logarithm
The Natural logarithm (LN) is used by clicking on the "LN" button or type "LN()".
Inverse
Multiplicative inverse (reciprocal function) is used by pressing the "1/x" button or typing "inv()". This function is the same as x^-1 or dividing 1 by the number.
Exponent
Numbers with exponents of 10 are displayed with an "e", for example 4.5e+100 or 4.5e-100. This function represents 10^x. Numbers are automatically displayed in the format when the number is too large or too small for the display. To enter a number in this format use the exponent key "EEX". To do this enter the mantissa (the non exponent part) then press "EEX" or type"e" and then enter the exponent.
Factorial
The Factorial function is used by clicking the "!" button or type "!".
PI
PI is a mathematical constant of the ratio of a circle's circumference to its diameter.
TABLE OF CONTENTS
Ø INTRODUCTION
Ø CODING
Ø APPLICATIONS & FUTUREPROSPECTIVE
Ø REFERENCES
CODING
#include
#include
#include
#include
#include
#include
#include
#include
#define pi 3.1415265
union REGS i,o;
int sr,dpf;
char *no[]={"1","2","3","4","5","6","7","8","9","0",".","+/-"},
*cal[]={"+","-","*","/","=","ã"},
*sci[]={"Sin","Cos","Tan","Sinh","Cosh","Tanh","Exp","ln","log","xrty","1/x","x^2","x^y","sqrt","fact","Hypot","eqn","DEG",},
*ms[]={"AC","HEX","BIN","OCT","BKSP"};
long com(long,int);
long double back(long double),equ(),alg(long double,int);
double ns(long double,int);
int box(int,int,int,int,int);
char *z2;
long double *z1;
int xy1[3];
void draw() //-----DRAW THE BODY OF CALCULATOR
{
int gm,gd=DETECT;
int x,y,x1,y1,i,j;
initgraph(&gd,&gm,"c:\\tc\\bgi"); //INITIALISE GRAPHICS
z2=(char * ) malloc(sizeof(char)*10); /*ALLOCATE MEMORY TO z2*/
x=getmaxx();y=getmaxy();
setcolor(DARKGRAY); setfillstyle(1,CYAN); //CYAN outer body
floodfill(5,5,DARKGRAY);
setcolor(BLACK);setfillstyle(1,LIGHTGRAY);
rectangle(20,20,x-20,y-20); //grey calculator body
floodfill(50,50,BLACK);
setcolor(BLACK); //black outline
line(20,20,x-20,20);
line(20,20,20,y-20);
setcolor(BLUE);setfillstyle(1,BLUE);
rectangle(21,20,x-21,40);
floodfill(25,25,BLUE); /* blue quit rectangle*/
setcolor(BLACK);
outtextxy(x/5,8,"Scientific Calculator by-: Akash(02512) & Akhil(02514)");
initmouse();
showmouse();
setmouse(0,0);
setcolor(WHITE);setfillstyle(1,WHITE);
rectangle(30,55,x-30,70); //---white i/o box
floodfill(32,59,WHITE);
outtextxy(x-220,27,"Press Any Key To Quit."); //---Quit
setcolor(DARKGRAY);
line(235,95,235,y-30); //grey partition line
setfillstyle(1,LIGHTGRAY);
/*------------------printing nos.---------------------*/
i=0;
for(x1=40;x1<150;x1+=30)
{ j=0;
for(y1=100;y1<450;y1+=40)
{
box(x1,y1,40,WHITE,BLACK);
setcolor(BLUE);
if(i==1&&j==10)
outtextxy(x1+10,y1+20,no[i+j]);
else
outtextxy(x1+15,y1+20,no[i+j]);
y1+=20; j+=2;
}
i++;
x1+=40;
}
/*---------------------------------------------------------------*/
/*--------printing simple algebric functions:(+,-,*,/)----------*/
for(x1;x1<=180;x1+=40)
{ j=0;
for(y1=100;y1<450;y1+=40) /*x1=180*/
{
box(x1,y1,40,WHITE,BLACK);
setcolor(BLUE);
outtextxy(x1+15,y1+20,cal[j]);
y1+=20;
j++;
}
}
x1+=30;
/*-----------------------------------------------------------------*/
/*--------------------print scientific functions-------------------*/
i=0;
for(x1;x1<501;x1+=30)
{ j=0;
for(y1=100;y1<450;y1+=40)
{
box(x1,y1,70,WHITE,BLACK); /*x1=220*/
setcolor(BLUE);
outtextxy(x1+15,y1+20,sci[i+j]);
y1+=20; j+=3;
}
xy1[i]=x1; /*store X coordinates*/
i++;
x1+=70;
}
/*-----------------------------------------------------------------*/
/*------------------print MATHEMATICAL SYSTEMS: BIN,HEX-------------*/
for(x1;x1<=550;x1+=30)
{ j=0;
for(y1=100;y1<450;y1+=40) /*x1=550*/
{ if(j==5)
break;
box(x1,y1,55,WHITE,BLACK);
setcolor(RED);
outtextxy(x1+15,y1+20,ms[j]);
y1+=20;
j++;
}
}
mouse();
}
void main() //MAIN DECLARATION
{
password();
draw();
}
/*-----------MOUSE PROGRAMMING------------*/
mouse()
{
int button,x,y;
char s[13]={" "};
int x1,y1,i,j,flag=1,l;
long double n,k;
while(!kbhit())
{ Again:
getmouse(&button,&x,&y);
while(button==1)
{
getmouse(&button,&x,&y);
sr=1;
}
if(sr==1)
{
i=0;
sr=0;
if(x>=xy1[0]&&x<=(xy1[0]+70)) /*fourth column check*/
{
colm1(n,y);
dpf=0;
strcpy(s," ");
}
if(x>=xy1[1]&&x<=(xy1[1]+70)) /*fifth column check*/
{
colm2(n,y);
dpf=0;
strcpy(s," ");
}
if(x>=xy1[2]&&x<=(xy1[2]+70)) /*sixth column check*/
{
colm3(n,y);
dpf=0;
strcpy(s," ");
}
for(x1=40;x1<150;x1+=30) //1st & 2nd column check
{ j=0; setcolor(DARKGRAY);
for(y1=100;y1<450;y1+=40)
{ if(x>=x1 && y>=y1 && x<=x1+40 && y<=y1+40)
{ box(x1,y1,40,BLACK,WHITE);
delay(200);
box(x1,y1,40,WHITE,BLACK);
if((strcmp(no[i+j],no[11]))==0)
{ if(flag==1)
{ n*=-1; // +/- sign
s[0]='-';
flag=0;
}
else
{ n*=-1;
s[0]=' ';
setcolor(LIGHTGRAY);
setfillstyle(1,WHITE);
floodfill(32,59,LIGHTGRAY);
flag=1;
}
goto NEXT;
}
if(strlen(s)>=11)
goto Again;
if((strcmp(no[i+j],no[10]))==0)
{
if(dpf==0)
{
strcat(s,no[i+j]); //save no. to string s
dpf=1;
}
}
else
strcat(s,no[i+j]); //save no. to string s
NEXT:
n=_atold(s); //array to long double
setcolor(DARKGRAY);
outtextxy(30,60,s); // display no. in i/o box
goto Again;
}
y1+=20; j+=2;
}
i++;
x1+=40;
}
if(x>550 && x<605>340 && y<380) //BACKSPACE
{ delay(100);
setcolor(LIGHTGRAY);
setfillstyle(1,WHITE);
floodfill(32,59,LIGHTGRAY);
l=strlen(s);
if(s[l-1]=='.')
dpf=0;
s[l-1]=s[l];
setcolor(DARKGRAY);
outtextxy(30,60,s);
goto Again;
}
if(x>550 && x<605) // 7th column
{ setcolor(LIGHTGRAY);
setfillstyle(1,WHITE);
floodfill(32,59,LIGHTGRAY);
dpf=0;
ns(n,y);
strcpy(s," ");
goto Again;
}
if(x>180 && x<220) // 3rd column
{
setcolor(LIGHTGRAY);
setfillstyle(1,WHITE);
floodfill(32,59,LIGHTGRAY);
dpf=0;
if(y>400 && y<440) // pi value
{
box(180,400,40,BLACK,WHITE);
delay(200);
box(180,400,40,WHITE,BLACK);
n=pi;
setcolor(DARKGRAY);
outtextxy(30,60," 3.1415265");
goto Again;
}
alg(n,y);
strcpy(s," ");
goto Again;
}
}
}
return;
}
/*-------perform algebric calculations---------*/
long double alg(long double n, int y )
{
int y1;
static int i;
long double r;
z1[i]=n; //copy no. to z1
if(y>100 && y<140) //--add
{ box(180,100,40,BLACK,WHITE);
delay(200);
box(180,100,40,WHITE,BLACK); // add(n);
z2[i]=43;
i++;
return 0;
}
if(y>160 && y<200) //subtract
{ box(180,160,40,BLACK,WHITE);
delay(200);
box(180,160,40,WHITE,BLACK); // sub(n);
z2[i]=45;
i++;
return 0;
}
if(y>220 && y<260) //multiply
{ box(180,220,40,BLACK,WHITE);
delay(200);
box(180,220,40,WHITE,BLACK); //mul(n);
z2[i]=42;
i++;
return 0;
}
if(y>280 && y<320) //divide
{ box(180,280,40,BLACK,WHITE);
delay(200);
box(180,280,40,WHITE,BLACK); //div(n);
z2[i]=47;
i++;
return 0;
}
if(y>340 && y<380) //equal
{ box(180,340,40,BLACK,WHITE);
delay(200);
box(180,340,40,WHITE,BLACK);
z1[i+1]=z2[i]='\0';
equ();
i=0;
return 0;
}
return 0;
}
/*---------solve algebric functions--------*/
long double equ()
{
int i,j;
char ch[50]={" "};
for(i=0;z2[i]!='\0';)
{
if(z2[i]=='/') /*------perform division------*/
{ z1[i]/=z1[i+1];
for(j=i;z2[j]!='\0';j++)
{ z1[j+1]=z1[j+2];
z2[j]=z2[j+1];
}
}
else
i++;
} /*--------------*/
for(i=0;z2[i]!='\0';)
{
if(z2[i]=='*') /*------perform multiplication------*/
{
z1[i]*=z1[i+1];
for(j=i;z2[j]!='\0';j++)
{ z1[j+1]=z1[j+2];
z2[j]=(int)z2[j+1];
}
}
else
i++; /*--------------*/
}
for(i=0;z2[i]!='\0';)
{
if(z2[i]=='+') /*------perform addition------*/
{
if(z2[i-1]=='-')
z1[i+1]*=-1;
z1[i]+=z1[i+1];
for(j=i;z2[j]!='\0';j++)
{ z1[j+1]=z1[j+2];
z2[j]=z2[j+1];
}
}
else
i++; /*--------------*/
}
for(i=0;z2[i]!='\0';)
{
if(z2[i]=='-') /*------perform subtraction------*/
{
z1[i]-=z1[i+1];
for(j=i;z2[j]!='\0';j++)
{ z1[j+1]=z1[j+2];
z2[j]=z2[j+1];
}
}
else
i++;
} /*--------------*/
if(z2[1]=='r') /*------find yth roots------*/
z1[0]=pow(z1[2],1/z1[0]);
if(z2[1]=='p') /*------find yth power------*/
z1[0]=pow(z1[2],z1[0]);
if(z2[1]=='h') /*------find hypotenuse------*/
z1[0]=hypot(z1[2],z1[0]);
gcvt(z1[0],15,ch); /*------copy result to array----------*/
setcolor(DARKGRAY);
outtextxy(35,60,ch); //display result
press();
return 0;
}
/*-------perform numeric system calculations--------*/
double ns(long double b, int y )
{ int y1;
long n;
n=b;
if(y>100 && y<140) // AC function
{
box(550,100,55,BLACK,WHITE);
delay(200);
box(550,100,55,WHITE,BLACK);
return 0;
}
if( y>160 && y<200) // HEX function
{
box(550,160,55,BLACK,WHITE);
delay(200);
box(550,160,55,WHITE,BLACK);
com(n,16);
}
if( y>220 && y<260) // BINARY function
{
box(550,220,55,BLACK,WHITE);
delay(200);
box(550,220,55,WHITE,BLACK);
com(n,2);
}
if( y>280 && y<320) //OCTAL function
{
box(550,280,55,BLACK,WHITE);
delay(200);
box(550,280,55,WHITE,BLACK);
com(n,8);
}
return 0;
}
/*---------common for HEX, BINARY & OCTAL-------------*/
long com(long b,int k)
{
char *str;
int i=0;
itoa(b,str,k); // integer to array
if(k==16)
{
while(str[i]!='\0')
{
if(str[i]>96 && str[i]<103)
str[i]-=32;
i++;
}
}
setcolor(DARKGRAY);
outtextxy(35,60,str);
press();
return 0;
}
/*Program to find roots of a Quad. Eqn. */
roots( )
{
float a,b,c,disc,r1,r2,s,x,y;
int k=253;
closegraph();
restorecrtmode();
printf("Input values of a, b, c in ax%c+bx+c\n ",k);
scanf("%f%f%f",&a,&b,&c);
disc= b*b-4*a*c;
if(disc<0)
{
printf("\n roots are IMAGINERY \n");
s=-disc;
x=sqrt(s)/(2*a);
y=-b/(2*a);
printf("\n r1=%f+i%f",y,x);
printf("\n r2=%f-i%f",y,x);
}
else
{
r1=(-b+sqrt(disc))/(2.0*a);
r2=(-b-sqrt(disc))/(2.0*a);
printf("\n r1=%f \n r2=%f \n",r1,r2);
}
getch();
return;
}
/*---------------BUTTONS------------------------*/
int box(int x1,int y1,int l,int c1,int c2)
{
setcolor(c1);
setfillstyle(1,LIGHTGRAY);
rectangle(x1,y1,x1+l,y1+40);
floodfill(x1+3,y1+10,c1);
setcolor(c2);
line(x1+l,y1,x1+l,y1+40);
line(x1,y1+40,x1+l,y1+40);
return 0;
}
/*password at start screen*/
password()
{
int i,x=270,gm,gd=DETECT;
char ch,pass[10];
initgraph(&gd,&gm,"c:\\tc\\bgi");
rectangle(15,15,615,465);
setcolor(LIGHTBLUE);
setfillstyle(1,LIGHTBLUE);
floodfill(50,50,15);
settextstyle(1,HORIZ_DIR,3);
setcolor(BLACK);
outtextxy(200,50,"Enter the password");
for(i=0;i<=10;i++,x+=10)
{
ch=getch();
if(ch==13)
break;
outtextxy(x,150,"*");
sound(300);
delay(50);
nosound();
pass[i]=ch;
}
pass[i]='\0';
if(!strcmp(pass,"as")) //compare entered string with password
return 0;
else
cleardevice();
rectangle(15,15,615,465);
setcolor(LIGHTBLUE);
setfillstyle(1,LIGHTBLUE);
floodfill(50,50,15);
settextstyle(1,HORIZ_DIR,3);
setcolor(RED);
outtextxy(220,50,"Wrong Password");
outtextxy(80,150,"This program will terminate in 5 seconds");
for(i=5;i>=0;i--)
{
setcolor(LIGHTBLUE);
setfillstyle(1,LIGHTBLUE);
bar(300,240,330,300);
setcolor(RED);
outtextxy(310,250,itoa(i,pass,10));
sound(1000*i+500);
delay(300);
nosound();
delay(700);
}
exit(0);
return 0;
}
/*-----------solving scientific functions------------*/
//---the no. entered is in RADIANS
/*-----------check for first column------------------*/
colm1(long double a,int y)
{
double cal;
char *str;
z1[2]=a;
setcolor(WHITE); setfillstyle(1,WHITE);
bar(30,55,610,70);
if(y>=100 && y<=140) // SINE of entered no.
{
box(xy1[0],100,70,BLACK,WHITE);
delay(200);
box(xy1[0],100,70,WHITE,BLACK);
cal=sin(a);
}
if(y>=160 && y<=200) // HYPERBOLIC SINE of entered no.
{
box(xy1[0],160,70,BLACK,WHITE);
delay(200);
box(xy1[0],160,70,WHITE,BLACK);
cal=sinh(a);
}
if(y>=220 && y<=260) // EXPONENTIAL of entered no.
{
box(xy1[0],220,70,BLACK,WHITE);
delay(200);
box(xy1[0],220,70,WHITE,BLACK);
cal=exp(a);
}
if(y>=280 && y<=320) // Yth ROOT of entered no.
{
box(xy1[0],280,70,BLACK,WHITE);
delay(200);
box(xy1[0],280,70,WHITE,BLACK);
z2[1]='r';
return 0;
}
if(y>=340 && y<=380) // Yth POWER of entered no.
{
box(xy1[0],340,70,BLACK,WHITE);
delay(200);
box(xy1[0],340,70,WHITE,BLACK);
z2[1]='p';
return 0;
}
if(y>=400 && y<=440) // HYPOTENUSE of entered no.
{
box(xy1[0],400,70,BLACK,WHITE);
delay(200);
box(xy1[0],400,70,WHITE,BLACK);
z2[1]='h';
return 0;
}
setcolor(DARKGRAY);
gcvt(cal,10,str);
outtextxy(35,60,str);
press();
return(0);
}
/*-----------check for second column------------------*/
colm2(long double a,int y)
{
double cal;
int i;
char *str;
setcolor(WHITE); setfillstyle(1,WHITE);
bar(30,55,610,70);
if(y>=100 && y<=140) // COSINE of entered no.
{
box(xy1[1],100,70,BLACK,WHITE);
delay(200);
box(xy1[1],100,70,WHITE,BLACK);
cal=cos(a);
}
if(y>=160 &&y<=200) // HYPERBOLIC COSINE of entered no.
{
box(xy1[1],160,70,BLACK,WHITE);
delay(200);
box(xy1[1],160,70,WHITE,BLACK);
cal=cosh(a);
}
if(y>=220 && y<=260) // NATURAL LOG of entered no.
{
box(xy1[1],220,70,BLACK,WHITE);
delay(200);
box(xy1[1],220,70,WHITE,BLACK);
cal=log(a);
}
if(y>=280 && y<=320) // INVERSE of entered no.
{
box(xy1[1],280,70,BLACK,WHITE);
delay(200);
box(xy1[1],280,70,WHITE,BLACK);
cal=1/a;
}
if(y>=340 && y<=380) // SQRT of entered no.
{
box(xy1[1],340,70,BLACK,WHITE);
delay(200);
box(xy1[1],340,70,WHITE,BLACK);
cal=sqrt(a);
}
if(y>=400 && y<=440) // QUADRATIC EQN.
{
box(xy1[1],400,70,BLACK,WHITE);
delay(200);
box(xy1[1],400,70,WHITE,BLACK);
roots();
draw();
return 0;
}
setcolor(DARKGRAY);
gcvt(cal,10,str);
outtextxy(35,60,str);
press();
return 0;
}
/*-----------check for third column------------------*/
colm3(long double a,int y)
{
double cal;
char *str;
setcolor(WHITE); setfillstyle(1,WHITE);
bar(30,55,610,70);
if(y>=100 && y<=140) // TANGENT of entered no.
{ box(xy1[2],100,70,BLACK,WHITE);
delay(200);
box(xy1[2],100,70,WHITE,BLACK);
cal=tan(a);
}
if(y>=160 && y<=200) //HYPERBOLIC TANGENT of entered no.
{
box(xy1[2],160,70,BLACK,WHITE);
delay(200);
box(xy1[2],160,70,WHITE,BLACK);
cal=tanh(a);
}
if(y>=220 && y<=260) // LOG TO THE BASE 10 of entered no.
{
box(xy1[2],220,70,BLACK,WHITE);
delay(200);
box(xy1[2],220,70,WHITE,BLACK);
cal=log10(a);
}
if(y>=280 && y<=320) // SQUARE of entered no.
{
box(xy1[2],280,70,BLACK,WHITE);
delay(200);
box(xy1[2],280,70,WHITE,BLACK);
cal=pow(a,2);
}
if(y>=340 && y<=380) // FACTORIAL of entered no.
{
box(xy1[2],340,70,BLACK,WHITE);
delay(200);
box(xy1[2],340,70,WHITE,BLACK);
cal=1;
for(;a>=1;a--)
cal=cal*a;
}
if(y>=400 && y<=440) // conversion of DEGREES to RADIANS
{
box(xy1[2],400,70,BLACK,WHITE);
delay(200);
box(xy1[2],400,70,WHITE,BLACK);
cal=(180*a)/pi;
}
setcolor(DARKGRAY);
gcvt(cal,10,str);
outtextxy(35,60,str);
press();
return(0);
}
//Changing the blue rectangle contents
press()
{
int x;
x=getmaxx();
setcolor(BLACK);
setfillstyle(1,RED);
bar(21,20,x-21,40);
floodfill(25,25,BLACK); /* blue rectangle*/
setcolor(WHITE);
outtextxy(x-250,27,"Press Any Key To Continue"); /*---Continue---*/
getch();
setcolor(LIGHTGRAY);
setfillstyle(1,WHITE);
floodfill(32,59,LIGHTGRAY);
setcolor(BLACK);setfillstyle(1,BLUE);
rectangle(21,20,x-21,40);
floodfill(25,25,BLACK); /* blue rectangle*/
setcolor(WHITE);
outtextxy(x-220,27,"Press Any Key To Quit."); /*---Quit---*/
}
/*-----------------------END--------------------------------------*/
APPLICATIONS
In most countries, students use calculators for schoolwork. There was some initial resistance to the idea out of fear that basic arithmetic skills would suffer. There remains disagreement about the importance of the ability to perform calculations "in the head", with some curricula restricting calculator use until a certain level of proficiency has been obtained, while others concentrate more on teaching estimation techniques and problem-solving. Research suggests that inadequate guidance in the use of calculating tools can restrict the kind of mathematical thinking that students engage in. Others have argued that calculator use can even cause core mathematical skills to atrophy, or that such use can prevent understanding of advanced algebraic concepts.
There are other concerns - for example, that a pupil could use the calculator in the wrong fashion but believe the answer because that was the result given. Teachers try to combat this by encouraging the student to make an estimate of the result manually and ensuring it roughly agrees with the calculated result. Also, it is possible for a child to type in −1 × −1 and obtain the correct answer '1' without realizing the principle involved. In this sense, the calculator becomes a crutch rather than a learning tool, and it can slow down students in exam conditions as they check even the most trivial result on a calculator.
REFERENCES
- Thomas J. Bing, Edward F. Redish, Symbolic Manipulators Affect Mathematical Mindsets, December 2007
- ^ Mike Sebastian's calculator forensics algorithm is an example of such rounding errors -- the algorithm's arcsin(arccos(arctan(tan(cos(sin(9)))))) should come out 9 on standard floating point hardware, but for CORDIC it's a pathological case that produces different rounding errors on each chip that it is implemented on. The algorithm is primarily used to identify the manufacturer of a particular calculator's CPU, since it is usually reproducible between chips of the same model.
- ^ Georges Ifrah notes that humans learned to count on their hands. Ifrah shows, for example, a picture of Boethius (who lived 480–524 or 525) reckoning on his fingers in Ifrah 2000, p. 48.
- ^ According to Schmandt-Besserat 1981, these clay containers contained tokens, the total of which were the count of objects being transferred. The containers thus served as a bill of lading or an accounts book. In order to avoid breaking open the containers, marks were placed on the outside of the containers, for the count. Eventually (Schmandt-Besserat estimates it took 4000 years) the marks on the outside of the containers were all that were needed to convey the count, and the clay containers evolved into clay tablets with marks for the count.
- ^ Lazos 1994
- ^ Ancient Discoveries, Episode 11: Ancient Robots, History Channel, http://www.youtube.com/watch?v=rxjbaQl0ad8, retrieved on 6 September 2008
- ^ A Spanish implementation of Napier's bones (1617), is documented in Montaner i Simon 1887, pp. 19-20.
- ^ Kells, Kern & Bland 1943, p. 92
- ^ Kells, Kern & Bland 1943, p. 82, as log(2)=.3010, or 4 places.
- ^ Schmidhuber
- ^ As quoted in Smith 1929, pp. 180-181
- ^ Slide Rules
- ^ Smart Computing Article - Calculating Clock to Carnegie Mellon University
- ^ IBM Archives: IBM 608 calculator
- ^ "Simple and Silent", Office Magazine, Dec. 1961, p1244
- ^ "'Anita' der erste tragbare elektonische Rechenautomat" [trans: "the first portable electronic computer"], Buromaschinen Mechaniker, Nov. 1961, p207
- ^ Texas Instruments Celebrates the 35th Anniversary of Its Invention of the Calculator Texas Instruments press release, 15 Aug 2002.
- ^ Electronic Calculator Invented 40 Years Ago All Things Considered, NPR, 30 Sept 2007. Audio interview with one of the inventors.
- ^ "Single Chip Calculator Hits the Finish Line", Electronics's', Feb. 1 1971, p19
No comments:
Post a Comment